The Attempt at a Solution

|F| = sqroot( (0.288 N)^2 + (0.1 N)^2 ) = 0.304867 N *I know this is wrong because I tried to submit this answer and it was no go.*

Part B.
atan(0.1 N/0.288 N) = 19.148 degress
180 - 19.148 = 160.852 degress
*For this part I figured I take 180 and subtract the degrees obtained to get the degrees counter clockwise of the +x direction.

Homework Statement

|F| = sqroot( (0.288 N)^2 + (0.1 N)^2 ) = 0.304867 N *I know this is wrong because I tried to submit this answer and it was no go.*

This is wrong, because the forces from two charges are not perpendicular to each other. You need to find x and y components of each force, from those, get the x and y components of the resultant force, and then compute its magnitude and direction.